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Higher Dimensional Categories: from double to multiple categories / Macro Grandis

By: Grandis, Marco [author].
Publisher: New Jersey: World Scientific, 2019Description: xi, 522 pages, 23.5 cm.ISBN: 9789811205101.Subject(s): Algebraic CategoriesDDC classification: 512.6
Contents:
Introduction -- Part I From Categories to Double Categories -- A Review of Basic Category Theory -- Introducing Two-Dimensional Category Theory -- Double Categories -- Double Adjunctions -- Double Limits -- Part II Multiple Categories -- Weak and Lax Multiple Categories -- Multiple Adjunctions -- Monads and Algebras for Multiple Categories -- Appendix A -- Applications in Homological Algebra and Algebraic Topology -- Appendix B -- Symmetric Cubical Sets and Cubical Categories -- Appendix C -- Solutions and Hints -- References -- Index
Summary: This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.6 G753 (Browse shelf) Available 138470
Total holds: 0

Includes bibliographical references and index

Introduction --
Part I From Categories to Double Categories -- A Review of Basic Category Theory -- Introducing Two-Dimensional Category Theory -- Double Categories -- Double Adjunctions -- Double Limits --
Part II Multiple Categories -- Weak and Lax Multiple Categories -- Multiple Adjunctions -- Monads and Algebras for Multiple Categories --
Appendix A -- Applications in Homological Algebra and Algebraic Topology --
Appendix B -- Symmetric Cubical Sets and Cubical Categories --
Appendix C -- Solutions and Hints --
References --
Index

This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories.

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